龙贝格累加算法.cpp

龙格贝塔算法

#include <iostream.h>
#include <math.h>
double f(double);
void main()
{ 
 double a,b,e,r1,s1,c1,r2,c2,T2,s2;
	int k;
cout<<"请输入a的值"<<endl;
	cin>>a;
cout<<"请输入b的值"<<endl;
	cin>>b;
cout<<"请输入e的值"<<endl;
	cin>>e;
	double h=b-a;
	double T1=h/2*(f(a)+f(b));
	k=1;
	while (k>=1)
	{
	double s=0;
		double x=a+h/2;
		while(x<b)
		{
			s=s+f(x);
			x=x+h;
		}
		  T2=T1/2+h/2*s;
	 s2=T2+(T2-T1)/3;
          //double  s1;
		 while (k==1)
		 {
			 k=k+1;
			 h=h/2;
			 T1=T2;
			   s1=s2;
		 }
		   c2=s2+(s2-s1)/15;
         // double c1;
		  while (k==2)
		  {
			  c1=c2;
               k=k+1;
			   h=h/2;
			 T1=T2;
			 s1=s2;
		  }
		      r2=c2+(c2-c1)/63;
           //double r1;
			 while(k==3)
			 { r1=r2;
                c1=c2;
               k=k+1;
			   h=h/2;
			 T1=T2;
			 s1=s2;
			 }
			 
			   if((k>4)&&(r2-r1)*(r2-r1)<e*e)
			   {     cout<<"最终结果"<<r1;
				   cout<<"最终结果"<<r2;
				   break;
			   }
			       else
				   {  
                    r1=r2;
                    c1=c2;
                      k=k+1;
			         h=h/2;
			        T1=T2;
			        s1=s2;
				   }
	}
}
            double f( double x)
			 {return (4/(1+x*x));
			 }